Given a closed 3-manifold $M^3$ endowed with a radial symmetric metric of negative sectional curvature, we define the cross curvature flow on $M^3$; using the maximum principle theorem, we demonstrated that the solution to the cross curvature flow exists for all time and converges pointwise to a hyperbolic metric.
Cross curvature flow, geometric evolution equation, negative sectional curvature
"The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvature,"
Turkish Journal of Mathematics: Vol. 43:
5, Article 31.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss5/31